Many important problems in science and engineering involve inferring a signal from noisy and/or incomplete observations, where the observation process is known. Historically, this problem has been tackled using hand-crafted regularization (e.g., sparsity, total-variation) to obtain meaningful estimates. Recent data-driven methods often offer better solutions by directly learning a solver from examples of ground-truth signals and associated observations. However, in many real-world applications, obtaining ground-truth references for training is expensive or impossible. Self-supervised learning methods offer a promising alternative by learning a solver from measurement data alone, bypassing the need for ground-truth references. This manuscript provides a comprehensive summary of different self-supervised methods for inverse problems, with a special emphasis on their theoretical underpinnings, and presents practical applications in imaging inverse problems.

翻译：科学与工程中的许多重要问题都涉及从噪声和/或不完整的观测中推断信号，其中观测过程是已知的。历史上，这一问题通常通过手工设计的正则化方法（例如稀疏性、全变分）来获得有意义的估计。近期的数据驱动方法通过直接从真实信号及其对应观测的样本中学习求解器，往往能提供更好的解决方案。然而，在许多实际应用中，获取用于训练的真实参考数据成本高昂或根本不可行。自监督学习方法提供了一种有前景的替代方案，仅从测量数据中学习求解器，从而绕过了对真实参考数据的需求。本文全面总结了针对逆问题的不同自监督学习方法，特别强调了其理论基础，并展示了在成像逆问题中的实际应用。